All of the 4th grade teachers and students from Springer went on a field trip to an art museum. Tickets were $$6.00$ each for teachers and $$4.50$ each for students, and the group paid $$45.00$ in total. A few weeks later, the same group visited a science museum where the tickets cost $$24.00$ each for teachers and $$11.50$ each for students, and the group paid $$141.00$ in total. Find the number of teachers and students on the field trips.
Answer: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${6x+4.5y = 45}$ ${24x+11.5y = 141}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-4$ ${-24x-18y = -180}$ ${24x+11.5y = 141}$ Add the top and bottom equations together. $ -6.5y = -39 $ $ y = \dfrac{-39}{-6.5}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $ {6x+4.5y = 45}$ to find $x$ ${6x + 4.5}{(6)}{= 45}$ $6x+27 = 45$ $6x = 18$ $x = \dfrac{18}{6}$ ${x = 3}$ You can also plug ${y = 6}$ into $ {24x+11.5y = 141}$ and get the same answer for $x$ ${24x + 11.5}{(6)}{= 141}$ ${x = 3}$ There were $3$ teachers and $6$ students on the field trips.